Lens recommendation for tiger photography

I am planning to take a photography tour in India to photograph tiger and other animals. What lens would be recommended for such purpose?

I am canon user and have 5d mk iv with 100-400 IS I. I have 1.4x III extender. I can rent a 500mm lens if that’s recommended but I am not sure if such a long lens is the go to choice for photography in jungle where the animal may be close to me. I have no experience in this area, so I don’t know how close the encounters are, or how big the 500mm lens will zoom onto the biggest cat.

Any advise would be much appreciated. Any anecdotes from people who have photographed big cats in jungles would also be helpful. Thanks.